Pedestrians pass the Barneys New York department store on Monday. When a black teen came forward with a story of being detained after buying a $349 belt at the Manhattan luxury store, an already-fraught relationship between the New York Police Department and New York's minority communities became even more tense.

Civil rights activist Al Sharpton was to meet Tuesday with Barneys New York’s CEO to discuss allegations of racial profiling at the luxury store.

Mr. Sharpton, of the National Action Network, has threatened a boycott of Barneys, after two black shoppers came forward this week with allegations that in separate incidents police had detained them on suspicion of stealing their expensive purchases from the high-end retailer. His meeting with Barneys CEO Mark Lee was scheduled for Tuesday morning at the National Action Network’s headquarters in Harlem.

"Attorney General [Eric] Schneiderman is committed to ensuring that all New York residents are afforded equal protection under the law," Kristen Clarke, head of the attorney general's Civil Rights Bureau, wrote to the two retailers' CEOs.

"The alleged repeated behavior of your employees raises troubling questions about your company's commitment to that ideal," the letters said.

The developments come amid an already-troubled relationship between the New York Police Department and the city’s minority communities and has put another spotlight on the city's pushback against persistent racism.

Reports of racial profiling first surfaced last week when Trayon Christian, 19, a Queens student, filed suit against both Barneys and the NYPD in Manhattan Supreme Court for an alleged incident on April 29. In that incident, plainclothes officers stopped him a block away from the Barneys flagship store on Madison Avenue, where he had just purchased a $349 Ferragamo belt with his debit card, he said. He was held at the 19th Precinct for two hours before he was released, with no charges filed against him, he said.

Also, Kayla Phillips, 21, a nursing student from Canarsie in Brooklyn, told the New York Daily News that four plainclothes officers surrounded her three blocks from the same Barneys store, after she had purchased a $2,500 orange suede Céline bag with a debit card in February. Ms. Phillips said she plans to sue the NYPD.

Two Macy’s shoppers have made similar allegations of racial profiling. One of them, the actor Rob Brown of HBO's "Treme," said he was handcuffed and held for an hour after purchasing a $1,350 gold Movado watch at Macy's Herald Square, the Daily News said. In the other, Art Palmer, an exercise trainer from Brooklyn, said that police swarmed him after he purchased $320 worth of Polo shirts and ties at the same store, the Daily News reported.

Mr. Brown is suing the NYPD and Macy's. Mr. Palmer has filed a complaint with the Civilian Complaint Review Board in New York.

Macy's told the Daily News it was not involved in the incident with Brown. Barneys said in a statement that “no employee of Barneys New York was involved in the pursuit of any action with [Mr. Christian] other than the sale.”

“Barneys New York has zero tolerance for any form of discrimination and we stand by our long history in support of all human rights,” the statement said.

Following reports of the incidents, Change.org launched a petition asking Jay Z to cut all ties with Barneys, with which he is collaborating on a Christmas collection. When the superstar and man-of-the-street rapper made no immediate comment, he was pilloried on social media as betraying his previous stands for social justice.

In 2006, the Brooklyn native had banned Cristal champagne from his swanky nightclub after the company's CEO made racist remarks, the Daily News reported.

On Saturday, Jay Z defended his choice to continue working with Barneys, at least for the time being.

''I am against discrimination of any kind, but if I make snap [judgments], no matter who it's towards, aren't I committing the same sin as someone who profiles?” he wrote on his website, Life + Times, noting that a quarter of the proceeds from his collection would benefit the Shawn Carter Foundation, which helps low-income students.

“I am no stranger to being profiled and I truly empathize with anyone that has been put in that position,” he wrote. “Hopefully this brings forth a dialogue to effect real change.”

Racism has been a foregrounded issue in New York City in recent years, as pressure has mounted on the NYPD to ease its aggressive stop-and-frisk policies. In August, a federal judge ordered the NYPD to reform its stop-and-frisk program. Last month the judge, Shira Scheindlin of US District Court in Manhattan, also granted class-action status to a lawsuit brought by public housing residents and visitors who say they were illegally stopped in the buildings.